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Proof step 7 from proof pot-pot-02 (previous step)

0 ≤ j, 0 ≤ j0, 0 < j0, ∀ j1, j, i. i→n(j1) < i→n(j0) → 0 ≤ j ∧ 0 ≤ j1 → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (j * j0) = (i ^ j) ^ (j0 - 1) * i ^ j

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
j0 = i0 + 1, 0 ≤ j, 0 ≤ j0, 0 < j0, ∀ j1, j, i. i→n(j1) < i→n(j0) → 0 ≤ j ∧ 0 ≤ j1 → i ^ (j * j1) = (i ^ j) ^ j1 ⊦ i ^ (j * j0) = (i ^ j) ^ i0 * i ^ j

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [j0, 1, i0] flags:

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: j0, 1, i0